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i'm trying to find a mirror shape which focuses a light at some specific point [itex]x_0[/itex]

the initial equation i derived for determining the shape of the mirror is:

(assuming that light rays fall parallel to x axis - light source is very far from the mirror)

f(x) is the shape i'm trying to determine

[tex]

x_0=-\frac{f(x)-\tan(2\arctan(\frac{df}{dx}))x}{\tan(2\arctan(\frac{df}{dx}))}

[/tex]

basicly this is an expression for a line passing through point [itex]x_0[/itex] and point on

f(x) where light reflected.

so [itex]\tan(2\arctan(\frac{df}{dx}))[/itex] is a incline of this line

from the initial equation i got to this point and i'm not sure what to do next:

[tex]

\frac{f(x)}{x-x_0}=\tan(2\arctan(\frac{df}{dx}))

[/tex]

the initial equation i derived for determining the shape of the mirror is:

(assuming that light rays fall parallel to x axis - light source is very far from the mirror)

f(x) is the shape i'm trying to determine

[tex]

x_0=-\frac{f(x)-\tan(2\arctan(\frac{df}{dx}))x}{\tan(2\arctan(\frac{df}{dx}))}

[/tex]

basicly this is an expression for a line passing through point [itex]x_0[/itex] and point on

f(x) where light reflected.

so [itex]\tan(2\arctan(\frac{df}{dx}))[/itex] is a incline of this line

from the initial equation i got to this point and i'm not sure what to do next:

[tex]

\frac{f(x)}{x-x_0}=\tan(2\arctan(\frac{df}{dx}))

[/tex]

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